High Frequency Conductivity in the Quantum Hall Regime

We have measured the complex conductivity ${\sigma }_{\mathrm{xx}}$ of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that ${\sigma }_{\mathrm{xx}}$ can be scaled to a single function for different frequencies and several transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length $\xi$. Even for large filling factor distances $\delta \nu$ from the critical point we find $\xi \propto \delta {\nu }^{-\gamma }$ with a scaling exponent $\gamma =2.3\mathrm{}$.